Apparatus and method for estimating an amount of condensed water in an anode of a fuel cell system and method of controlling a drain valve using same

ABSTRACT

An apparatus for estimating an amount of condensed water in an anode of a fuel cell system includes: an initial anode water vapor amount calculation unit to calculate an initial amount of water vapor in the anode of a fuel cell upon startup, an anode diffusion amount calculation unit to calculate an amount of H 2 O diffused from a cathode to the anode, a purge amount calculation unit to calculate an amount of water vapor discharged upon gas purging in the anode, a recirculation amount calculation unit to calculate the amount of water vapor recirculated to the anode, and a condensed water amount determination and water level estimation unit to calculate the actual amount of water vapor in the anode based on values calculated using these units and to calculate the amount of condensed water in a water trap.

CROSS-REFERENCE TO THE RELATED APPLICATION

This application claims priority to and the benefit of Korean PatentApplication No. 10-2021-0119569, filed on Sep. 8, 2021, in the KoreanIntellectual Property Office, the disclosure of which is incorporatedherein by reference in its entirety.

BACKGROUND 1. Field

The present disclosure relates to a method of estimating the amount ofcondensed water in the anode of a fuel cell system and a method ofcontrolling a drain valve based on the estimated amount of condensedwater. More particularly, the present disclosure relates to an apparatusand method for estimating the amount of condensed water in the anode ofa fuel cell system capable of preventing malfunction of draining byaccurately calculating the amount of condensed water collected in awater trap and to a method of controlling a drain valve using the same.

2. Description of the Related Art

The statements in this section merely provide background informationrelated to the present disclosure and may not constitute prior art.

A fuel cell is a kind of power generator that directly converts chemicalenergy generated by oxidation of fuel into electrical energy. A fuelcell is basically the same as a chemical cell in that it uses oxidationand reduction reactions, but is different in that a reactant iscontinuously supplied from the outside and a reaction product iscontinuously removed from the system, unlike the chemical cell, in whichthe cell reaction is carried out inside a closed system. Since thereaction product of the fuel cell is pure water, thorough research intothe use thereof as an energy source for an eco-friendly vehicle isongoing.

The fuel cell system includes a fuel cell stack that generateselectrical energy through a chemical reaction, an air supply system thatsupplies air to the cathode of the fuel cell stack, and a hydrogensupply system that supplies hydrogen to the anode of the fuel cellstack.

When power is generated in the fuel cell stack, product water isgenerated inside the fuel cell stack, and a portion thereof passesthrough the electrolyte membrane due to the concentration difference andis discharged to the anode. In the hydrogen supply system, hydrogen gasis recirculated using a recirculator, and the product water dischargedfrom the anode is condensed and stored in a water trap included in thehydrogen supply system. The water trap includes a water level sensor,and when the amount of condensed water exceeds a preset water level, thedrain valve is opened to discharge the stored condensed water to theoutside of the fuel cell stack.

FIG. 1 schematically illustrates the configuration of a system thatprovides a water trap with a water level sensor to discharge the storedcondensed water.

The water level sensor provided to the water trap is configured todirectly measure the level of condensed water in the water trap. Here,when the value measured by the water level sensor reaches at a fulllevel (3 mm), the drain valve is opened to empty the water trap. On theother hand, the water level sensor may be configured to close the drainvalve when it is confirmed that the lowest water level (a mm) has beenreached.

As illustrated in FIG. 1 , in the system that controls opening andclosing of the drain valve using the water level sensor, the amount ofcondensed water in the water trap may be determined based only on thesensor value, so the water level does not match with the actual waterlevel due to a slope or a traveling road or dynamic behavior of avehicle (i.e. a sudden stop or sudden start). Hence, frequentopening/closing of the valve may occur unintentionally, and stackflooding may occur due to deterioration of discharge performance ofcondensed water. This may cause deterioration of stack durability andcell drop due to insufficient reactive gas supply.

Moreover, in the system that relies on the water level sensor, even whenthe amount of condensed water is the minimum level, a drain valve may beexcessively opened by erroneous detection due to fluctuation ofcondensed water, which may cause a problem in which the concentration ofexhaust gas increases.

SUMMARY

The present disclosure provides an apparatus and method for estimatingthe amount of condensed water in the anode of a fuel cell system, inwhich the actual amount of condensed water in a water trap may beaccurately calculated in the fuel cell system configured to collectcondensed water in the water trap and to discharge the collectedcondensed water through a drain valve.

The present disclosure also provides an apparatus and method forestimating the amount of condensed water in the anode of a fuel cellsystem, in which the actual amount of condensed water collected in awater trap may be accurately estimated, thus preventing malfunction ofdraining due to a slope of a traveling road or dynamic behavior of avehicle (i.e. a sudden stop/acceleration or sudden start) duringdraining, thereby preventing stack flooding and an increase in theconcentration of exhaust gas.

In addition, the present disclosure provides an apparatus for estimatingthe amount of condensed water in the anode of a fuel cell system havinga reduced manufacturing cost due to elimination of the water levelsensor from the water trap.

In one form of the present disclosure, a method of estimating an amountof condensed water in an anode of a fuel cell system includes:calculating an initial amount of water vapor in an anode of a fuel cellupon startup, calculating an amount of H₂O diffused from a cathode tothe anode during power generation by the fuel cell, calculating anamount of water vapor discharged upon gas purging in the anode duringpower generation by the fuel cell, and calculating an amount of watervapor recirculated to the anode during power generation by the fuelcell. In particular, an actual amount of water vapor in the anode iscalculated based on values calculated in respective steps, and an amountof condensed water in a water trap is calculated based on a differencebetween the calculated actual amount of water vapor in the anode and anamount of saturated water vapor in the anode at a current temperature.

In calculating the initial amount of water vapor in the anode uponstartup, the initial amount of water vapor in the anode may becalculated based on an ideal gas equation using a saturated water vaporpressure of the anode at a stack temperature as a current water vaporpressure of the anode.

In calculating the amount of H₂O diffused from the cathode to the anode,a vapor diffusion rate due to a vapor pressure difference between thecathode and the anode may be integrated over time to thereby calculatean amount of diffused water vapor between the cathode and the anode. Thecalculated amount of diffused water vapor may be determined to be theamount of H₂O diffused from the cathode to the anode.

In calculating the amount of H₂O diffused from the cathode to the anode,a correction factor (K, 0≤K≤1) for compensating for an amount of H₂Odischarged to the outside of a stack among H₂O generated at the cathodemay be determined, and a corrected amount of diffused water vapor,obtained by multiplying the calculated amount of diffused water vapor bythe correction factor, may be determined to be the amount of H₂Odiffused from the cathode to the anode.

In one form, the correction factor may be a value selected using apredetermined map depending on a degree of opening of an air pressurecontrol valve connected to an air outlet and a rotation speed of an aircompressor.

In calculating the amount of water vapor discharged upon purging, theamount of water vapor discharged upon purging may be calculated bymultiplying a total gas purge rate by a molar fraction of water vapor toobtain a water vapor purge rate and integrating the water vapor purgerate over time.

In calculating the amount of water vapor recirculated to the anode, theamount of water vapor recirculated to the anode may be calculated bymultiplying a total amount of recirculated gas, determined depending ona hydrogen supply pressure and a stack current, by a partial pressure ofwater vapor in a gas in the anode.

A water trap water level (%) may be additionally calculated based on avolume ratio of the calculated amount of condensed water in the watertrap and an internal volume of the water trap. For the volume ratiocalculation, the calculated amount of condensed water in the water trapis covered into a volume.

In addition, the present disclosure provides a method of controlling adrain valve using the method of estimating the amount of condensed waterin the anode of a fuel cell system, further including determining awater trap water level (%) based on a volume ratio of the calculatedamount of condensed water in the water trap and an internal volume ofthe water trap. Thus, when a water level determined in the water trapexceeds a reference water level value, the drain valve is opened todischarge condensed water, and when an accumulated purge amount exceedsa reference purge amount, the drain valve is closed.

In another form of the present disclosure, an apparatus for estimatingan amount of condensed water in an anode of a fuel cell system includes:an initial anode water vapor amount calculation unit configured tocalculate an initial amount of water vapor in an anode of a fuel cellupon startup, an anode diffusion amount calculation unit configured tocalculate an amount of H₂O diffused from a cathode to the anode duringpower generation by the fuel cell, a purge amount calculation unitconfigured to calculate an amount of water vapor discharged upon gaspurging in the anode during power generation by the fuel cell, arecirculation amount calculation unit configured to calculate an amountof water vapor recirculated to the anode during power generation by thefuel cell, and a condensed water amount determination and water levelestimation unit configured to calculate an actual amount of water vaporin the anode based on values calculated using the initial anode watervapor amount calculation unit, the anode diffusion amount calculationunit, the purge amount calculation unit, and the recirculation amountcalculation unit and to calculate an amount of condensed water in awater trap based on a difference between the calculated actual amount ofwater vapor in the anode and an amount of saturated water vapor in theanode at a current temperature.

The initial anode water vapor amount calculation unit may be configuredsuch that the initial amount of water vapor in the anode is calculatedbased on an ideal gas equation using a saturated water vapor pressure ofthe anode at a stack temperature as a current water vapor pressure ofthe anode, the anode diffusion amount calculation unit may be configuredsuch that an amount of diffused water vapor between the cathode and theanode is calculated by integrating a vapor diffusion rate due to a vaporpressure difference between the cathode and the anode over time, thepurge amount calculation unit may be configured such that the amount ofwater vapor discharged upon purging is calculated by multiplying a totalgas purge rate by a molar fraction of water vapor to obtain a watervapor purge rate and integrating the water vapor purge rate over time,and the recirculation amount calculation unit may be configured suchthat the amount of water vapor recirculated to the anode is calculatedby multiplying a total amount of recirculated gas, determined dependingon a hydrogen supply pressure and a stack current, by a partial pressureof water vapor in a gas in the anode.

The anode diffusion amount calculation unit may be configured such thata correction factor (K, 0≤K≤1) for compensating for an amount of H₂Odischarged to the outside of a stack among H₂O generated at the cathodeis determined and a corrected amount of diffused water vapor, obtainedby multiplying the calculated amount of diffused water vapor by thecorrection factor, is determined to be the amount of H₂O diffused fromthe cathode to the anode, and the correction factor may be a valueselected using a predetermined map depending on a degree of opening ofan air pressure control valve connected to an air outlet and a rotationspeed of an air compressor.

The condensed water amount determination and water level estimation unitmay be configured such that a water trap water level (%) is additionallycalculated based on a volume ratio of the calculated amount of condensedwater in the water trap and an internal volume of the water trap.

In one form, when a water level determined in the water trap using thecondensed water amount determination and water level estimation unitexceeds a reference water level value, a drain valve opening command maybe transmitted to a controller, and when an accumulated purge amountexceeds a reference purge amount, a drain valve closing command may betransmitted to the controller.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other objects, features and other advantages of thepresent disclosure should be more clearly understood from the followingdetailed description taken in conjunction with the accompanyingdrawings, in which:

FIG. 1 illustrates the configuration of a conventional system includinga water trap provided with a water level sensor and a drain valve thatdischarges condensed water;

FIG. 2 illustrates the configuration of a fuel cell system including anapparatus for estimating the amount of condensed water in an anodeaccording to an embodiment of the present disclosure;

FIG. 3 is a graph illustrating transmission of a draining terminationcommand depending on the cumulative purge amount in a process ofcontrolling a drain valve using a process of estimating the amount ofcondensed water in the anode of a fuel cell system according to anembodiment of the present disclosure; and

FIG. 4 is a flowchart illustrating the process of estimating the amountof condensed water in the anode of a fuel cell system according to anembodiment of the present disclosure and the process of controlling adrain valve using the same.

The drawings described herein are for illustration purposes only and arenot intended to limit the scope of the present disclosure in any way.

DETAILED DESCRIPTION

The following description is merely exemplary in nature and is notintended to limit the present disclosure, application, or uses. Itshould be understood that throughout the drawings, correspondingreference numerals indicate like or corresponding parts and features.

When a component, device, element, or the like of the present disclosureis described as having a purpose or performing an operation, function,or the like, the component, device, or element should be consideredherein as being “configured to” meet that purpose or to perform thatoperation or function.

As publicly known in the art, some of exemplary forms may be illustratedin the accompanying drawings from the viewpoint of function blocks,units and/or modules. Those having ordinary skill in the art shouldunderstand that such blocks, units and/or modules are physicallyimplemented by electronic (or optical) circuits such as logic circuits,discrete components, processors, hard wired circuits, memory devices andwiring connections. When the blocks, units and or modules areimplemented by processors or other similar hardware, the blocks, unitsand modules may be programmed and controlled through software (forexample, codes) in order to perform various functions discussed in thepresent disclosure.

Reference is now be made in detail to an apparatus and method forcorrecting a pressure sensor offset of a fuel cell system according tovarious embodiments of the present disclosure, examples of which areillustrated in the accompanying drawings.

FIG. 2 illustrates the configuration of a fuel cell system including anapparatus for estimating the amount of condensed water in an anodeaccording to an embodiment of the present disclosure.

With reference to FIG. 2 , an air supply system 20 configured to supplyair is connected to the cathode of a fuel cell stack 10, and a hydrogensupply system 30 configured to supply hydrogen is connected to the anodethereof.

The air supply system 20 may include an air compressor 21 configuredsuch that outdoor air is sucked, compressed, and transferred to ahumidifier, and a humidifier 22 configured such that the compressed airis humidified to thereby be imparted with appropriate humidity. The airhaving passed through the humidifier 22 reacts with hydrogen at an anode12 while passing through a cathode 11 via an air supply line 23. As thehumidifier 22, a membrane humidifier, performing water exchange betweenthe water in wet gas discharged after fuel cell reaction and the airsupplied from the outside, may be mainly used. To this end, the airdischarged from the cathode outlet may be supplied again to thehumidifier 22 through an air return line 24. Moreover, an air pressurecontrol valve 26 is provided at one side of the humidifier 22, and thewet air not participating in humidification is discharged to the outsidealong an air exhaust line 27 via the air pressure control valve 26. Theair pressure control valve 26 may serve to control the pressure of airsupplied to the cathode by adjusting the rotation speed of the aircompressor 21 or by adjusting the degree of opening of the valveindependently thereof.

In the hydrogen supply system 30, hydrogen supplied through a hydrogensupply valve 31 is supplied to the anode 12 through an ejector 32 and ahydrogen supply line 33. Pressure sensors 41, 42 configured to detectpressure may be disposed upstream and downstream of the ejector 32.

Meanwhile, some hydrogen not participating in the reaction, among thehydrogen supplied to the anode, may be recirculated upstream of theanode through a hydrogen recirculation line 34 and supplied again to theanode. Here, condensed water in the anode is discharged together withthe hydrogen not participating in the reaction, and a water trap 35configured to collect this condensed water is provided at the anodeoutlet side.

A drain valve 36 is provided downstream of the water trap 35, andcondensed water may be discharged to the outside through the drain valve36. As such, condensed water discharged through the drain valve 36 maybe discharged to the outside along the air exhaust line 27, and may betransferred to the humidifier 22 of the air supply system and used forhumidification, as illustrated in FIG. 1 .

A controller 50 controls the operation of the fuel cell system based oninformation obtained using various sensors 41, 42, 43, 44 in the fuelcell system, and generally controls operable components in the fuel cellsystem, such as the air compressor 21 and various valves 25, 26, 31, 36.

In addition, the fuel cell system illustrated in FIG. 2 includes anapparatus 60 for estimating the amount of condensed water in the anode.

This apparatus 60 for estimating the amount of condensed water in theanode is configured such that the actual amount of water vapor in theanode is calculated based on various pieces of data in the fuel cellsystem and the amount of condensed water expected to be condensed due tooversaturation of water vapor in the anode is estimated based thereon.In one embodiment of the present disclosure, as illustrated in FIG. 2 ,the apparatus 60 for estimating the amount of condensed water in theanode includes an initial anode water vapor amount calculation unit 61,an anode diffusion amount calculation unit 62, a purge amountcalculation unit 63, a recirculation amount calculation unit 64, and acondensed water amount determination and water level estimation unit 65.

In particular, the apparatus for estimating the amount of condensedwater in the anode is configured such that the initial amount of watervapor in the anode upon startup is estimated and then the amount ofwater vapor expected to be condensed due to oversaturation is calculatedas the amount of condensed water collected in the water trap, inconsideration of the change in the amount of water vapor in the anodeduring power generation.

Hereinafter, a process of calculating the amount of water vapor usingindividual units in the apparatus for estimating the amount of condensedwater in the anode and a process of estimating the amount of condensedwater in the water trap based on the calculated amount of water vaporare described in detail.

Specifically, the initial anode water vapor amount calculation unit 61may be configured to calculate the initial amount of water vapor in theanode of a fuel cell upon startup. Since the initial anode is inequilibrium with the system temperature, it may be assumed that it issaturated at a relative humidity of 100% based on a stack coolanttemperature. Moreover, the initial amount of water vapor in the anodemay be determined based on the ideal gas equation using the volume ofthe anode (V_(an)), the stack coolant temperature (T), corresponding tothe stack temperature, and the water vapor pressure of the anode(P_(an, v)). Briefly, the initial number of moles of water vapor in theanode (n_(an)) may be calculated using Equation 1 below.

$\begin{matrix}{n_{on} = \frac{P_{{an},v} \times V_{an}}{RT}} & \left\lbrack {{Equation}1} \right\rbrack\end{matrix}$

(n_(an) is the initial number of moles of water vapor in the anode,P_(an, v) is the water vapor pressure of the anode, V_(an) is the volumeof the anode, T is the stack coolant temperature, and R is the gasconstant, that is, 8.314 [j/mol·K].)

Assuming saturation at a relative humidity of 100%, the water vaporpressure of the anode (P_(anH2O)) is the same as the saturated watervapor pressure of the anode, so the initial number of moles of watervapor in the anode (n_(an)) in Equation 1 may be calculated based on thesaturated water vapor pressure of the anode, the stack coolanttemperature (stack temperature), and the volume of the anode. Therefore,the initial anode water vapor amount calculation unit 61 may calculatethe initial amount of water vapor in the anode based on the ideal gasequation using the saturated water vapor pressure of the anode at thestack temperature as the current water vapor pressure of the anode.

In addition, the anode diffusion amount calculation unit 62 may beconfigured to calculate the amount of H₂O diffused from the cathode tothe anode during power generation by the fuel cell. In particular, theanode diffusion amount calculation unit 62 may be configured such thatthe water vapor diffusion rate due to the difference in water vaporpressure between the cathode and the anode is integrated over time tothereby calculate the amount of water vapor diffused between the cathodeand the anode, and the calculated amount of diffused water vapor may bedetermined to be the amount of H₂O diffused from the cathode to theanode.

Specifically, the diffusion of H₂O generated at the cathode to the anodeis caused by the differential pressure between the water vapor pressureof the cathode and the water vapor pressure of the anode. Since therelative humidity (RH) is “current water vapor amount/saturated watervapor amount*100”, the water vapor pressure of the cathode (P_(ca,V))may be obtained from a relative humidity estimate calculated using aknown cathode relative humidity estimator.

Accordingly, the water vapor pressure of the cathode (P_(ca,V)) may becalculated using Equation 2 below.

P _(ca,v) =P _(caH2Osat) λRH estimate  [Equation 2]

(P_(ca,V) is the water vapor pressure of the cathode, P_(caH2Osat) isthe saturated water vapor pressure of the cathode, and RH estimate isthe value calculated using a cathode relative humidity estimator (theactual relative humidity value of the cathode).)

With regard to Equation 2, the saturated water vapor pressure of thecathode is a function of the stack coolant temperature (corresponding tothe stack temperature), and may be obtained using the saturated watervapor pressure calculation equation.

The number of moles of water vapor diffused between the cathode and theanode may be determined by calculating a water vapor diffusion ratebetween the cathode and the anode using Equation 3 below and integratingthe water vapor diffusion rate over time.

$\begin{matrix}{{Ca}‐{{{An}{water}{vapor}{diffusion}{rate}\left( n_{vxo}^{\prime} \right)} = {\frac{D_{v}}{RT}\frac{P_{{ca},v} - p_{{an},v}}{\delta}A \times K}}} & \left\lbrack {{Equation}3} \right\rbrack\end{matrix}$

(n′_(v xo) is the cathode-anode water vapor diffusion rate, D_(v) is thewater vapor diffusion coefficient, K is the correction factor, A is thecatalyst area, and δ is the diffusion distance.)

In calculating the Ca—An vapor diffusion rate, diffusion is assumed tooccur due to the differential pressure, but some of H₂O generated at thecathode has no choice but to be discharged to the outside of the stackthrough the air outlet, so some H₂O is not diffused but is discharged tothe outside of the stack. Accordingly, it is desired to compensate forthe amount of H₂O that is discharged to the outside of the stack, and inthe present disclosure, the correction factor (K, 0≤K≤1) is applied.

Because the amount of H₂O discharged to the outside of the stack variesdepending on the supplied air flow rate and the applied pressure, thecorrection factor K may be a value selected using a predetermined mapdepending on the rotation speed of the air compressor (or a flow rate ofair by the air compressor) and the degree of opening of the air pressurecontrol valve connected to the air outlet to control the air pressure.

In addition, the purge amount calculation unit 63 may be configured tocalculate the amount of water vapor discharged upon gas purging in theanode during power generation by the fuel cell. The purge amountcalculation unit 63 may be configured such that the amount of watervapor discharged upon purging is calculated by multiplying a total gaspurge rate by a molar fraction of water vapor to obtain a water vaporpurge rate and integrating the water vapor purge rate over time.

Specifically, the number of moles of water vapor discharged upon purging(n_(v purge)) may be determined by calculating a water vapor purge rateusing Equation 4 below and integrating the water vapor purge rate overtime.

$\begin{matrix}{{{Water}{vapor}{purge}{rate}\left( n_{v{purge}}^{\prime} \right)} = {n_{purge}^{\prime} \times \frac{n_{v}}{n_{an}}}} & \left\lbrack {{Equation}4} \right\rbrack\end{matrix}$

(n′_(v purge) is the water vapor purge rate, n′_(purge) is the gas purgerate, and n_(v)/n_(an) is the molar fraction of water vapor.)

In addition, the recirculation amount calculation unit 64 may beconfigured to calculate the amount of water vapor recirculated to theanode during power generation by the fuel cell. In particular, therecirculation amount calculation unit 64 may calculate the amount ofwater vapor that is recirculated to the anode by multiplying the totalamount of recirculated gas, determined depending on the hydrogen supplypressure and the stack current, by the partial pressure of water vaporin gas in the anode.

In this regard, map data on the total amount of recirculated gas mappedto the ejector design specification criteria, the supply pressure (thevalue of the nozzle pressure sensor 41 or the stack inlet hydrogenpressure sensor 42), and the stack current may be utilized. Therefore,the total amount (number of moles) of recirculated gas may be determinedbased on map data of the total amount (number of moles) of recirculatedgas depending on the stack current and the supplied hydrogen pressure,and the determined total amount of recirculated gas may be multiplied bythe partial pressure value of water vapor in the mixed gas in the anode,thereby calculating the final amount of recirculated water vapor(Equation 5 below).

$\begin{matrix}{{{Number}{of}{moles}{of}{recirculated}{water}{vapor}\left( n_{v{rec}} \right)} = {n_{rec} \times \frac{n_{v}}{n_{an}}}} & \left\lbrack {{Equation}5} \right\rbrack\end{matrix}$

(n_(v rec) is the number of moles of recirculated water vapor, n_(rec)is the total amount of recirculated gas, and n_(v)/n_(an) is the molarfraction of water vapor.)

Based on the number of moles of water vapor calculated using theindividual units described above, the condensed water amountdetermination and water level estimation unit 65 may be configured tocalculate the actual amount of water vapor in the anode and to calculatethe amount of condensed water in the water trap based on the differencebetween the actual amount of water vapor in the anode thus calculatedand the amount of saturated water vapor in the anode at the currenttemperature.

Specifically, the number of moles of water vapor calculated using theinitial anode water vapor amount calculation unit 61 is referred to as“{circle around (1)}”, the number of moles of water vapor calculatedusing the anode diffusion amount calculation unit 62 is referred to as“{circle around (2)}”, the amount of purged water vapor calculated usingthe purge amount calculation unit 63 is referred to as “{circle around(3)}”, and the amount of recirculated water vapor calculated using therecirculation amount calculation unit 64 is referred to as “{circlearound (4)}”.

In the calculation of the current actual amount of water vapor in theanode using {circle around (1)} to {circle around (4)} as describedabove, the amount of purged water vapor and the amount of recirculatedwater vapor are the values to be subtracted, whereas the initial amountof water vapor in the anode “{circle around (2)}” and the amount ofwater vapor diffused from the cathode to the anode “{circle around (2)}”are the values to be added.

Therefore, the current actual amount of water vapor in the anode may bedetermined to be “{circle around (1)}+{circle around (2)}−{circle around(3)}−{circle around (4)}”. Moreover, the current amount of water vaporexpected to be condensed due to oversaturation in the anode, that is,the amount of condensed water collected in the anode water trap, may bethe value obtained by subtracting the “amount of saturated water vaporin the anode” from the current actual amount of water vapor in the anode“{circle around (1)}+{circle around (2)}−{circle around (3)}−{circlearound (4)}”. In this regard, since the value calculated based on{circle around (1)} to {circle around (4)} as described above is thenumber of moles of water vapor, the mass of condensed water may becalculated by multiplying the values of {circle around (1)} to {circlearound (4)} by the molar mass of water. For reference, if the ‘currentamount of water vapor expected to be condensed due to oversaturation inthe anode’ is a negative value, it is processed as ‘0’.

Accordingly, the amount of condensed water in the water trap may bedetermined as described above using the condensed water amountdetermination and water level estimation unit 65.

Moreover, the condensed water amount determination and water levelestimation unit 65 may be configured such that the water trap waterlevel (%) is additionally calculated based on a volume ratio of thecalculated amount of condensed water in the water trap and an internalvolume of the water trap. For the volume ratio calculation, thecalculated amount of condensed water in the water trap may be convertedinto a volume thereof.

Based on the equation “water trap water level (%)=volume of condensedwater/volume of water trap×100”, the water trap water level may bedetermined by calculating the ratio of the converted volume of condensedwater to the internal volume of the water trap using the condensed wateramount determination and water level estimation unit 65.

Meanwhile, opening and closing of a drain valve may be controlled basedon the calculated amount of condensed water and the water levelestimation results using the apparatus for estimating the amount ofcondensed water in the anode.

The method of controlling the drain valve may be performed in a mannerin which, when the water level exceeds a certain level, the drain valveis opened, whereas when the water level decreases below a referencelevel, the drain valve is closed, as in the conventional case in which awater level sensor is used.

For example, when the water level determined in the water trap using thecondensed water amount determination and water level estimation unit 65exceeds a reference water level value (B %), a drain valve openingcommand may be transmitted to the controller, and the controller, havingreceived the drain valve opening command, may directly open the drainvalve.

On the other hand, when the condensed water is drained and thus thewater level of the water trap reaches the lowest level, the drain valvehas to be closed again.

An integrated valve having both purging and draining functions isconfigured such that condensed water is always discharged first when thedrain valve is opened, and after completion of discharge of condensedwater, the mixed gas in the anode is discharged to the atmosphere.Therefore, in a system that does not have a valve position sensor or atrap water level sensor, when the accumulated value for the purge amountestimate reaches at least a certain value after the valve openingcommand, it may be determined that water discharge is completed and themixed gas in the anode has been discharged (purged). In the presentdisclosure, the accumulated value for the purge amount estimate may beset as a reference value for closing a valve, and a drain valve closingcommand may be executed accordingly.

In an embodiment of the present disclosure, the drain valve may becontrolled to be closed when the accumulated purge amount exceeds areference purge amount “A”. To this end, the apparatus for estimatingthe amount of condensed water in the anode may transmit a drain valveclosing command to the controller when the accumulated purge amountexceeds the reference purge amount.

With regard thereto, FIG. 3 is a graph illustrating transmission of adraining termination command depending on the cumulative purge amountafter start of draining. As illustrated in FIG. 3 , after start ofdraining (opening of the drain valve), draining may be terminated (thedrain valve may be closed) at the time point at which the accumulatedpurge amount exceeds the reference purge amount A.

FIG. 4 is a flowchart illustrating the process of estimating the amountof condensed water in the anode of a fuel cell system according to anembodiment of the present disclosure and the process of controlling adrain valve using the same.

In particular, as illustrated in FIG. 4 , steps S410 to S440 showestimation of the amount of condensed water in the anode and the waterlevel, and steps S450 to S480 generally show a draining control methodfor controlling opening and closing of the drain valve based on theresults of estimation of water level in the water trap. Therefore,although FIG. 4 illustrates both the process of estimating the amount ofcondensed water in the anode and the water level and the process ofcontrolling the drain valve, the present disclosure is not limitedthereto, and it should be clearly stated that the method of estimatingthe amount of condensed water in the anode up to step S430 and themethod of estimating the water level in the water trap up to step S440may be performed separately.

In particular, since respective calculation processes in steps S421 toS425 are specified in the above description of the apparatus forestimating the amount of condensed water in the anode, a redundantdescription thereof is omitted. However, those of having ordinary skillin the art should be able to fully understand that in performing stepsS421 to S425, the description of the apparatus for estimating the amountof condensed water in the anode may be equally applied.

When briefly describing individual steps, the method of estimating theamount of condensed water in the anode of the fuel cell system accordingto an embodiment of the present disclosure and the method of controllingthe drain valve using the same may include the following steps.

In the state in which power is able to be generated by the fuel cellsystem after completion of startup of the fuel cell, calculation of theinitial amount of water vapor in the anode of the fuel cell upon startupusing the initial anode water vapor amount calculation unit 61 (S421),calculation of the amount of H₂O diffused from the cathode to the anodeduring power generation by the fuel cell using the anode diffusionamount calculation unit 62 (S422), calculation of the amount of watervapor discharged upon gas purging in the anode during power generationby the fuel cell using the purge amount calculation unit 63 (S423), andcalculation of the amount of water vapor recirculated to the anodeduring power generation by the fuel cell using the recirculation amountcalculation unit 64 (S424) may be performed.

Moreover, calculation of the actual amount of water vapor in the anodebased on the values calculated through steps S421 to S424 as describedabove (S425) and calculation of the amount of condensed water (number ofmoles of condensed water) in the water trap (S430) based on thedifference between the actual amount of water vapor in the anodecalculated through step S420 and the amount of saturated water vapor inthe anode at the current temperature may be performed.

Thereafter, a water trap water level (%) is estimated based on a volumeratio of the calculated amount of condensed water in the water trap andan internal volume of the water trap (S440), and when the determinedwater level in the water trap exceeds a reference water level value(S450), the drain valve is opened, whereby the condensed water isdischarged (S460).

After discharge of a sufficient amount of condensed water through theopen drain valve, when the accumulated purge amount exceeds a referencepurge amount (S470), the drain valve is closed (S480).

Thereby, the amount of condensed water and the water level in the watertrap may be accurately estimated without the need to provide a waterlevel sensor to the water trap at the anode side of the fuel cellsystem, so efficient control of opening and closing of the drain valvebecomes possible.

As is apparent from the above description, in the apparatus and methodfor estimating the amount of condensed water in the anode of a fuel cellsystem according to the present disclosure, it is possible to eliminatea water level sensor applied to detect the water level in a water trapwhen conventionally controlling opening/closing of a drain valve,thereby reducing the cost of manufacturing the fuel cell system.

In addition, according to the present disclosure, the actual amount ofcondensed water collected in the water trap can be accurately estimated,thereby preventing malfunction of draining due to a road slope ordynamic behavior of a vehicle (e.g., a sudden stop or sudden start)during draining.

Thereby, in the method of controlling the drain valve according to thepresent disclosure, it is possible to fundamentally prevent malfunctionof draining on a slope or the like, thus preventing deterioration ofstack durability due to stack flooding and cell drop. Moreover, fuel canbe prevented from being excessively discharged through the drain valve,thereby preventing an increase in the concentration of exhaust gas.

Although the some embodiments of the present disclosure have beendisclosed for illustrative purposes, those having ordinary skill in theart should appreciate that various modifications, additions andsubstitutions are possible, without departing from the scope and spiritof the present disclosure.

What is claimed is:
 1. A method of estimating an amount of condensedwater in a fuel cell system, the method comprising: calculating aninitial amount of water vapor in an anode of a fuel cell upon startup;calculating an amount of H₂O diffused from a cathode to the anode duringpower generation by the fuel cell; calculating an amount of water vapordischarged upon gas purging in the anode during the power generation bythe fuel cell; and calculating an amount of water vapor recirculated tothe anode during the power generation by the fuel cell, wherein anactual amount of water vapor in the anode is calculated based on thecalculated amount of the diffused H₂O, the calculated amount of thedischarged water vapor, and the calculated amount of the recirculatedwater vapor, and wherein an amount of condensed water in a water trap iscalculated based on a difference between the calculated actual amount ofwater vapor in the anode and an amount of saturated water vapor in theanode at a current temperature.
 2. The method according to claim 1,wherein: in calculating the initial amount of water vapor in the anodeupon startup, the initial amount of water vapor in the anode iscalculated based on an ideal gas equation using a saturated water vaporpressure of the anode at a stack temperature as a current water vaporpressure of the anode.
 3. The method according to claim 1, wherein: incalculating the amount of H₂O diffused from the cathode to the anode, awater vapor diffusion rate due to a water vapor pressure differencebetween the cathode and the anode is integrated over time to therebycalculate an amount of diffused water vapor between the cathode and theanode, and the calculated amount of diffused water vapor is determinedto be the amount of H₂O diffused from the cathode to the anode.
 4. Themethod according to claim 3, wherein: in calculating the amount of H₂Odiffused from the cathode to the anode, a correction factor (K, 0≤K≤1)for compensating for an amount of H₂O discharged to an outside of a fuelcell stack among H₂O generated at the cathode is determined, and acorrected amount of diffused water vapor, obtained by multiplying thecalculated amount of diffused water vapor by the correction factor, isdetermined to be the amount of H₂O diffused from the cathode to theanode.
 5. The method according to claim 4, wherein the correction factoris a value selected using a predetermined map based on a degree ofopening of an air pressure control valve connected to an air outlet anda rotation speed of an air compressor.
 6. The method according to claim1, wherein: in calculating the amount of water vapor discharged uponpurging, the amount of water vapor discharged upon purging is calculatedby multiplying a total gas purge rate by a molar fraction of water vaporto obtain a water vapor purge rate and by integrating the water vaporpurge rate over time.
 7. The method according to claim 1, wherein: incalculating the amount of water vapor recirculated to the anode, theamount of water vapor recirculated to the anode is calculated bymultiplying a total amount of recirculated gas, determined depending ona hydrogen supply pressure and a stack current, by a partial pressure ofwater vapor in a gas in the anode.
 8. The method according to claim 1,wherein a water trap water level (%) is additionally calculated based ona volume ratio of the calculated amount of condensed water in the watertrap and an internal volume of the water trap.
 9. A method ofcontrolling a drain valve of a fuel cell system, the method comprising:calculating an initial amount of water vapor in an anode of a fuel cellupon startup; calculating an amount of H₂O diffused from a cathode tothe anode during power generation by the fuel cell; calculating anamount of water vapor discharged upon gas purging in the anode duringthe power generation by the fuel cell; calculating an amount of watervapor recirculated to the anode during the power generation by the fuelcell; calculating an amount of condensed water in a water trap based ona difference between an actual amount of water vapor in the anodecalculated and an amount of saturated water vapor in the anode at acurrent temperature, wherein the actual amount of water vapor in theanode is calculated based on the calculated amount of the diffused H₂O,the calculated amount of the discharged water vapor, and the calculatedamount of the recirculated water vapor; determining a water trap waterlevel (%) based on a volume ratio of the calculated amount of condensedwater in the water trap and an internal volume of the water trap;opening the drain valve to discharge condensed water when a water leveldetermined in the water trap exceeds a reference water level value; andclosing the drain valve when an accumulated purge amount exceeds areference purge amount.
 10. The method according to claim 9, wherein:the initial amount of water vapor in the anode is calculated based on anideal gas equation using a saturated water vapor pressure of the anodeat a stack temperature as a current water vapor pressure of the anode.11. The method according to claim 9, wherein: in calculating the amountof H₂O diffused from the cathode to the anode, a water vapor diffusionrate due to a water vapor pressure difference between the cathode andthe anode is integrated over time to thereby calculate an amount ofdiffused water vapor between the cathode and the anode, and thecalculated amount of diffused water vapor is determined to be the amountof H₂O diffused from the cathode to the anode.
 12. The method accordingto claim 11, wherein: calculating the amount of H₂O diffused from thecathode to the anode includes: determining a correction factor (K,0≤K≤1) for compensating for an amount of H₂O discharged to an outside ofa fuel stack among H₂O generated at the cathode, and determining acorrected amount of diffused water vapor as the amount of H₂O diffusedfrom the cathode to the anode, wherein the corrected amount of diffusedwater vapor is obtained by multiplying the calculated amount of diffusedwater vapor by the correction factor.
 13. The method according to claim12, wherein the correction factor is a value selected using apredetermined map depending on a degree of opening of an air pressurecontrol valve connected to an air outlet and a rotation speed of an aircompressor.
 14. The method according to claim 9, wherein: in calculatingthe amount of water vapor discharged upon purging, the amount of watervapor discharged upon purging is calculated by multiplying a total gaspurge rate by a molar fraction of water vapor to obtain a water vaporpurge rate and by integrating the water vapor purge rate over time. 15.The method according to claim 9, wherein: in calculating the amount ofwater vapor recirculated to the anode, the amount of water vaporrecirculated to the anode is calculated by multiplying a total amount ofrecirculated gas, determined based on a hydrogen supply pressure and astack current, by a partial pressure of water vapor in a gas in theanode.
 16. An apparatus for estimating an amount of condensed water in afuel cell system, comprising: an initial anode water vapor amountcalculation unit configured to calculate an initial amount of watervapor in an anode of a fuel cell upon startup; an anode diffusion amountcalculation unit configured to calculate an amount of H₂O diffused froma cathode to the anode during power generation by the fuel cell; a purgeamount calculation unit configured to calculate an amount of water vapordischarged upon gas purging in the anode during the power generation bythe fuel cell; a recirculation amount calculation unit configured tocalculate an amount of water vapor recirculated to the anode during thepower generation by the fuel cell; and a condensed water amountdetermination and water level estimation unit configured to calculate anactual amount of water vapor in the anode based on values calculatedusing the initial anode water vapor amount calculation unit, the anodediffusion amount calculation unit, the purge amount calculation unit,and the recirculation amount calculation unit and configured tocalculate an amount of condensed water in a water trap based on adifference between the calculated actual amount of water vapor in theanode and an amount of saturated water vapor in the anode at a currenttemperature.
 17. The apparatus according to claim 16, wherein: theinitial anode water vapor amount calculation unit is configured tocalculate the initial amount of water vapor in the anode based on anideal gas equation using a saturated water vapor pressure of the anodeat a stack temperature as a current water vapor pressure of the anode,the anode diffusion amount calculation unit is configured to calculatean amount of diffused water vapor between the cathode and the anode byintegrating a vapor diffusion rate over time, the purge amountcalculation unit is configured to calculate the amount of water vapordischarged upon purging by multiplying a total gas purge rate by a molarfraction of water vapor to obtain a water vapor purge rate andintegrating the water vapor purge rate over time, and the recirculationamount calculation unit is configured to calculate the amount of watervapor recirculated to the anode by multiplying a total amount ofrecirculated gas, which is determined depending on a hydrogen supplypressure and a stack current, by a partial pressure of water vapor in agas in the anode.
 18. The apparatus according to claim 17, wherein: theanode diffusion amount calculation unit is configured to: determine acorrection factor (K, 0≤K≤1) for compensating for an amount of H₂Odischarged to an outside of a fuel stack among H₂O generated at thecathode, and determine a corrected amount of diffused water vapor as theamount of H₂O diffused from the cathode to the anode, wherein thecorrected amount of diffused water vapor is obtained by multiplying thecalculated amount of diffused water vapor by the correction factor, andwherein the correction factor is a value selected using a predeterminedmap based on a degree of opening of an air pressure control valveconnected to an air outlet and a rotation speed of an air compressor.19. The apparatus according to claim 16, wherein the condensed wateramount determination and water level estimation unit is configured tocalculate a water trap water level (%) based on a volume ratio of thecalculated amount of condensed water in the water trap and an internalvolume of the water trap.
 20. The apparatus according to claim 19,wherein: when a water level determined in the water trap using thecondensed water amount determination and water level estimation unitexceeds a reference water level value, a drain valve opening command istransmitted to a controller, and when an accumulated purge amountexceeds a reference purge amount, a drain valve closing command istransmitted to the controller.